Even Function:
Eg: f(x)=x2−1 is an even function.
Odd Function:
If f(-x) = -f(x) then we call that function as Odd function. In the graph of odd function, the first and third quadrants will be reflections of each other and so will the second and fourth quadrant.
Eg: f(x)=x3−x
Modulus function:
The function defined by f(x) = |x| ={x−xx≥0x<0 is called the modulus function. The Domain of |x| = R and Range = R+ U {0}, i.e. set of all non-negative real numbers.
Greatest integer function:
For any real number x, we denote [x], the greatest integer less than or equal to x. For example,
[2.45] = 2 and [– 2.1] = – 3. The function defined by f(x) = [x] for all x ∈ R is called the greatest integer function. Obviously, the Domain of [x] = R and the Range = Z, i.e. set of integers.
Square root function:
A function f(x) defined by f(x) = √x, x∈R+ is called the square root function. The Domain and Range of the square root function is [0, ∞) which is set of all non-negative real numbers.
Signum function:
The function defined by f (x) = {|x|x0x≠0x=0{1−10x>0x<0x=0 is called the signum function also given by sgn(x). The Domain = R and Range = {– 1, 0, 1}.
Polynomial function:
A function of the form f(x) = a0xn+a1xn−1+......+an−1xn−1+an, where a0,a1...an an are real numbers, a0≠0and n∈N, is called a polynomial function of degree n. The Domain of a polynomial function is R. Range can be any subset of real numbers.
Reciprocal function:
The function that associates each non-zero real number x to its reciprocal, i.e. f(x) = 1x is called the reciprocal function. Domain = Range = R – {0}.